What is the front wave?

The front wave precedes the formation stage of the low. The closing of the first isobar around the top of the wave is a sign of the formation of a young low. As it develops it becomes a mature low when the occlusion of atmospheric fronts begins.
The low is a vortex. For a vortex to form from a front wave, it must be fed by cyclonic vorticity. It may come from a heat source; a typical area for such a source is the Mediterranean Sea in the cold season, or from a jet stream - in the latter case, the season is irrelevant.